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针对状态和控制输入均含有时滞的离散时间系统,提出最优跟踪控制的设计方法.通过引入一种新的状态向量,将含有状态和控制输入时滞的离散时间系统转化为含有虚拟扰动项的无时滞离散时间系统.根据最优控制理论,构造离散Riccati矩阵方程和离散Stein矩阵方程的序列,并证明该解序列一致收敛于变换后的离散时间系统的最优跟踪控制策略.利用最优控制的逐次逼近设计方法,得到最优跟踪控制的近似解,并给出求解最优跟踪控制律的算法.仿真算例表明了所提出最优跟踪控制方法的有效性.
Aiming at the discrete-time system with time-delay state and control inputs, a design method of optimal tracking control is proposed. By introducing a new state vector, the discrete-time system with state and control input delay is transformed into a system with virtual disturbance term Based on the optimal control theory, the discrete Riccati matrix equation and the discrete Stein matrix equation sequence are constructed, and the optimal tracking control strategy is proved to converge uniformly to the transformed discrete-time system. And the approximate solution to the optimal tracking control is obtained and the algorithm for solving the optimal tracking control law is given.The simulation results show the effectiveness of the proposed tracking control method.